Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with a = 3.1%. A random sample of 10 bank stocks gave the following yields (in percents). 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is u = 4.2%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.2%? Use a = 0.01. (a) What is the level of significance? .01 State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O H: = 4.2%; H,: u # 4.2%; two-tailed H,: = 4.2%; H,A > 4.2%; right-tailed O H,: H = 4.2%; H,: u < 4.2%; left-tailed O H,: H > 4.2%; H,: µ = 4.2%; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since we assume that x has a normal distribution with unknown a. O The Student's t, since n is large with unknown a. O The standard normal, since we assume that x has a normal distribution with known a. O The Student's t, since we assume that x has a normal distribution with known o. Compute the z value of the sample test statistic. (Round your answer to two decimal places.) 1.17 (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) 1210

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
icon
Concept explainers
Question
Need help with the last 2 at the bottom with red x
Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with
o- 3,1%. A random sample of 10 bank stocks gave the following yields (in percents).
5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1
The sample mean is x= 5.38%. Suppose that for the entire stock market, the mean dividend yield is p = 4.2%. Do these data
indicate that the dividend yield of all bank stocks is higher than 4.2%? Use a = 0.01.
(a) What is the level of significance?
01
State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
O H,: u = 4.2%; H,: u # 4.2%; two-tailed
• H,: = 4.2%; H,: p > 4.2%; right-tailed
O H,: = 4.2%; H,: u < 4.2%; left-tailed
O H,: > 4.2%; H: = 4.2%; right-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
O The standard normal, since we assume that x has a normal distribution with unknown a.
O The Student's t, since n is large with unknown a.
O The standard normal, since we assume that x has a normal distribution with known a.
O The Student's t, since we assume that x has a normal distribution with known a.
Compute the z value of the sample test statistic. (Round your answer to two decimal places.)
117
) Find (or estimate) the P-value. (Round your answer to four decimal places.)
1210
Transcribed Image Text:Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with o- 3,1%. A random sample of 10 bank stocks gave the following yields (in percents). 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample mean is x= 5.38%. Suppose that for the entire stock market, the mean dividend yield is p = 4.2%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.2%? Use a = 0.01. (a) What is the level of significance? 01 State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O H,: u = 4.2%; H,: u # 4.2%; two-tailed • H,: = 4.2%; H,: p > 4.2%; right-tailed O H,: = 4.2%; H,: u < 4.2%; left-tailed O H,: > 4.2%; H: = 4.2%; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since we assume that x has a normal distribution with unknown a. O The Student's t, since n is large with unknown a. O The standard normal, since we assume that x has a normal distribution with known a. O The Student's t, since we assume that x has a normal distribution with known a. Compute the z value of the sample test statistic. (Round your answer to two decimal places.) 117 ) Find (or estimate) the P-value. (Round your answer to four decimal places.) 1210
Expert Solution
Step 1

Given information

Sample mean = 5.38%

Population mean µ = 4.2%

Sample size = 10

Standard deviation σ = 3.1%

Significance level (α) = 0.01

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Application of Integration
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman